Problem
Suppose that the current market value of a firm is 150. The firm lasts for two periods. The rate of return on the assets of the firm, over one period, is either 20% or -20% with equal probabilities. The riskless rate of interest is 5% in each period. If any cash payout, coupon and/or dividend, is made at the end of the first period, then the ex-payout firm value will change by either 20% or -20% over the second period.
1. Consider a callable bond with the coupon rate of 6.56% and the face value of 100. The call price on an ex-coupon basis is 100. What is the price of this callable bond? The firm pays no dividends on the stock at the end of the first period.
2. What is the price of the callable bond in part (1) if the firm pays dividends of 5 on the stock at the end of the first period?
3. What is the price of the callable bond in part (1) if the call premium follows a declining call schedule on an ex-coupon basis? The call price is 102 at the beginning of the first period, 101 at the end of the first period, and 100 at the end of the second period. The firm pays no dividends on the stock at the end of the first period.